This is the wiki for the Year 11 Mathematics Specialist 3A/3B course at St Stephen's School. (If you are looking for the Sadler Solutions, see http://maths.prideaux.id.au/sadlers/ instead.)
Automatically generated differentiation exercises. Practice your differentiation of polynomials using these computer-generated problems (with solutions when you're ready). You can work with simple polynomials or practice the product rule, the quotient rule or the chain rule or do mixed exercise sets. (Note that this page makes extensive use of MathML, a mathematics markup language that is not widely supported by browsers, especially versions more than a year or two old. It is known to work with recent versions of Mozilla Firefox. If you encounter problems, try downloading the latest version of Firefox.)
For some chapters there are not enough problems in the text book to provide the required amount of practice for students to begin to achieve mastery. So here are some more. (Note that the answers provided have not been thoroughly checked and there may be errors. Please let me know.)
Absolute value problems (answers). Note that there are some kinds of problems that are not included here. For instance, problems like |x-4|=|4-2x| don't appear here. You should try writing some of these problems yourself and then solving them. You might like to create a page in the student notes to share some of your problems.
Adding vectors (answers). These problems deal with writing one vector in terms of others, using the principles of adding vectors but without necessarily assigning any numerical values.
From time to time I will add to this page things like dates for coming tests or due dates for assignments: the sort of thing I write in the top right corner of the whiteboard in our classroom. I may also add links to documents like revision sheets or assignments so if you lose the copy I give you in class you can download yourself another copy. (That way I don't have to growl at you for being disorganised.)
Each class member is expected to contribute to a set of class notes for that class. I've written more about what should go into these in the expectations page.
Learning mathematics can be thought of as comprising two parts: developing a mental concept and building skills mastery. These two parts are equally important.
The skills mastery comes from rehearsal---i.e. practicing a skill until it becomes automatic. That's what you are doing when you are working through most of the exercises in the text book. For most people this is pretty easy, although it can be boring and time consuming.
Developing a mental concept is trickier. Because it's something that happens entirely in your mind, it happens differently for different people. To achieve this, it's not enough to know how to do a skill, you have to understand why you do it that way. A well-developed mental concept links new learning to other mathematics that you already know to produce a complex, inter-linked web of knowledge. The ability to build these rich mental concepts is the most important distinguishing feature of students who are good at maths. It's what you must strive for to achieve at this level of mathematics.
An example of this is the FOIL mnemonic you used when you were learning to expand expressions like (x+2)(x-5). Anyone can learn to do the First, Outside, Inside, Last product to correctly expand these, but you haven't really learned it unless you genuinely understand why you do it that way as well as when it's appropriate to use and when it isn't. When you have this mental concept firmly in place you are not thrown when you see something a bit different, and you can see, for instance, how to extend the method to be able to expand expressions like (x+y-3)(3x-y+2). In fact, when you truly have the mental concept in place, you don't need the FOIL mnemonic any more: you know how to do it because you understand.
To help you work on this, I am building a suite of Non-Routine Problems. These are problems that do not need any skills other than those covered in the course but are presented in such a way that it is not obvious what skills are needed or how to begin. You will need to call upon your mental concept to solve them. You should treat them as puzzles to solve: exercise persistence; try several different approaches; keep coming back to them until you crack them.
Table of Contents
3A/3B Mathematics Specialist wiki
This is the wiki for the Year 11 Mathematics Specialist 3A/3B course at St Stephen's School. (If you are looking for the Sadler Solutions, see http://maths.prideaux.id.au/sadlers/ instead.)Year 12 Mathematics Specialist
If you are doing Mathematics Specialist in Year 12, see the Year 12 3C/3C MAS wiki.Program
Solutions to tests, etc.
These have now been moved to a separate Solutions page.Exam Revision
Semester 1 Exam Revision work has been moved to a separate page.Sadler Solutions
The Sadler Solutions have been moved to their own page at http://maths.prideaux.id.au/sadlers/. Please update bookmarks.Term 3 Week 10 work
The work for Term 3 Week 10 is posted here for the benefit of the students on tour.Additional Problems
Automatically generated differentiation exercises. Practice your differentiation of polynomials using these computer-generated problems (with solutions when you're ready). You can work with simple polynomials or practice the product rule, the quotient rule or the chain rule or do mixed exercise sets. (Note that this page makes extensive use of MathML, a mathematics markup language that is not widely supported by browsers, especially versions more than a year or two old. It is known to work with recent versions of Mozilla Firefox. If you encounter problems, try downloading the latest version of Firefox.)For some chapters there are not enough problems in the text book to provide the required amount of practice for students to begin to achieve mastery. So here are some more. (Note that the answers provided have not been thoroughly checked and there may be errors. Please let me know.)
- Absolute value problems (answers). Note that there are some kinds of problems that are not included here. For instance, problems like |x-4|=|4-2x| don't appear here. You should try writing some of these problems yourself and then solving them. You might like to create a page in the student notes to share some of your problems.
- Adding vectors (answers). These problems deal with writing one vector in terms of others, using the principles of adding vectors but without necessarily assigning any numerical values.
From time to time I will add to this page things like dates for coming tests or due dates for assignments: the sort of thing I write in the top right corner of the whiteboard in our classroom. I may also add links to documents like revision sheets or assignments so if you lose the copy I give you in class you can download yourself another copy. (That way I don't have to growl at you for being disorganised.)Your part: Class Notes
Each class member is expected to contribute to a set of class notes for that class. I've written more about what should go into these in the expectations page.Non-Routine Problems
Learning mathematics can be thought of as comprising two parts: developing a mental concept and building skills mastery. These two parts are equally important.The skills mastery comes from rehearsal---i.e. practicing a skill until it becomes automatic. That's what you are doing when you are working through most of the exercises in the text book. For most people this is pretty easy, although it can be boring and time consuming.
Developing a mental concept is trickier. Because it's something that happens entirely in your mind, it happens differently for different people. To achieve this, it's not enough to know how to do a skill, you have to understand why you do it that way. A well-developed mental concept links new learning to other mathematics that you already know to produce a complex, inter-linked web of knowledge. The ability to build these rich mental concepts is the most important distinguishing feature of students who are good at maths. It's what you must strive for to achieve at this level of mathematics.
An example of this is the FOIL mnemonic you used when you were learning to expand expressions like (x+2)(x-5). Anyone can learn to do the First, Outside, Inside, Last product to correctly expand these, but you haven't really learned it unless you genuinely understand why you do it that way as well as when it's appropriate to use and when it isn't. When you have this mental concept firmly in place you are not thrown when you see something a bit different, and you can see, for instance, how to extend the method to be able to expand expressions like (x+y-3)(3x-y+2). In fact, when you truly have the mental concept in place, you don't need the FOIL mnemonic any more: you know how to do it because you understand.
To help you work on this, I am building a suite of Non-Routine Problems. These are problems that do not need any skills other than those covered in the course but are presented in such a way that it is not obvious what skills are needed or how to begin. You will need to call upon your mental concept to solve them. You should treat them as puzzles to solve: exercise persistence; try several different approaches; keep coming back to them until you crack them.
Other links